{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00000-a09a1d0c-1197-4369-851d-f7409bfe896e",
    "output_cleared": false
   },
   "source": [
    "# Phase-space file (PHSP)\n",
    "\n",
    "Use the output of the following simulation:\n",
    "- Folder: 3_linac/\n",
    "- Already computed results in folder output_ref/\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:06.171850Z",
     "start_time": "2024-01-23T19:55:05.788487Z"
    },
    "cell_id": "00001-da98f9a5-10a2-4e23-b64b-b7305982a0d4",
    "execution_millis": 297,
    "execution_start": 1605009800829,
    "output_cleared": false,
    "source_hash": "2036bae7"
   },
   "outputs": [],
   "source": [
    "# Tell Jupyter to plot figure right in the page\n",
    "# %matplotlib notebook\n",
    "\n",
    "# Module with plot capabilities\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Module with scientific computing functions (matrix/vector)\n",
    "import numpy as np                \n",
    "\n",
    "# Module to read root files\n",
    "import uproot\n",
    "\n",
    "# Modules with reading/write folder/file functions\n",
    "import os\n",
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:06.176577Z",
     "start_time": "2024-01-23T19:55:06.172539Z"
    },
    "cell_id": "00002-6af52d4a-45a2-415f-94c9-c9282735e2d9",
    "execution_millis": 3,
    "execution_start": 1605009801128,
    "output_cleared": false,
    "source_hash": "909ee571"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Current Working Directory (CWD) is: \n",
      " /Users/dsarrut/src/gate/dqprm/2025/gate-exercices/3_linac\n"
     ]
    }
   ],
   "source": [
    "# The following command display the current working directory (where jupyter has been launched)\n",
    "cwd = os.getcwd()\n",
    "print('The Current Working Directory (CWD) is: \\n', cwd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:19.240374Z",
     "start_time": "2024-01-23T19:55:16.949153Z"
    },
    "cell_id": "00003-5822b599-07ee-455c-8cf0-863f2de7f49b",
    "execution_millis": 61,
    "execution_start": 1605009813330,
    "output_cleared": false,
    "scrolled": true,
    "source_hash": "fe0e75b0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read PHSP object <TTree 'PhaseSpace' (8 branches) at 0x000110710d70>\n",
      "PhaseSpace keys:  ['KineticEnergy', 'Weight', 'PrePositionLocal_X', 'PrePositionLocal_Y', 'PrePositionLocal_Z', 'PreDirectionLocal_X', 'PreDirectionLocal_Y', 'PreDirectionLocal_Z']\n",
      "PhaseSpace numbers of elements:  5521465.0\n"
     ]
    }
   ],
   "source": [
    "# read a PHSP\n",
    "root_filename = Path('./data/phsp_1M.root')\n",
    "try:\n",
    "    f = uproot.open(root_filename)\n",
    "except Exception:\n",
    "    print(\"File '\"+root_filename+\"' cannot be opened, not root file ?\")\n",
    "    exit()\n",
    "\n",
    "# Look for a single key named \"PhaseSpace\"\n",
    "k = f.keys()\n",
    "try:\n",
    "    psf = f['PhaseSpace']\n",
    "except Exception:\n",
    "    print(\"This root file is not a PhaseSpace, keys are: \", f.keys())\n",
    "    exit()\n",
    "    psf = f['PhaseSpace']\n",
    "# now, the variable psf contains a root Tree with various branches: Energy, X, Y, Z etc\n",
    "print('Read PHSP object', psf)\n",
    "print(\"PhaseSpace keys: \", psf.keys())\n",
    "print(\"PhaseSpace numbers of elements: \", psf.num_entries)\n",
    "# all branches are set in the variable 'a'\n",
    "a = psf.arrays()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:19.347750Z",
     "start_time": "2024-01-23T19:55:19.242466Z"
    },
    "cell_id": "00004-ff22fa1e-88a1-46f4-8fbd-47c761a976e6",
    "execution_millis": 481,
    "execution_start": 1605009815199,
    "output_cleared": false,
    "source_hash": "7756d4f1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.03, 0.599, 1.24, 2.86, 0.386, 2.07, ..., 0.248, 0.891, 1.75, 0.805, 0.232]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1159122a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the E\n",
    "nbs = 200\n",
    "x = a['KineticEnergy']\n",
    "fig1, ax1 = plt.subplots()\n",
    "print(x)\n",
    "n, bins, patches = ax1.hist(x, nbs, density=True, alpha=0.75, label='E')\n",
    "ax1.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:19.361205Z",
     "start_time": "2024-01-23T19:55:19.346186Z"
    },
    "cell_id": "00005-cf0c295b-5872-44c2-8a4d-a674bbb1fb0a",
    "execution_millis": 181,
    "execution_start": 1605009816015,
    "output_cleared": false,
    "source_hash": "4dcc46f7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of elements:  5521465\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x115d27ad0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the X,Y \n",
    "nbs = 200\n",
    "x = a['PrePositionLocal_X']\n",
    "y = a['PrePositionLocal_Y']\n",
    "print('Number of elements: ', len(x))\n",
    "# only keep 500 first elements \n",
    "n = 500\n",
    "x = x[:n]\n",
    "y = y[:n]\n",
    "fig2, ax2 = plt.subplots()\n",
    "ax2.scatter(x, y, alpha=0.75, label='x y')\n",
    "ax2.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:19.557007Z",
     "start_time": "2024-01-23T19:55:19.361317Z"
    },
    "cell_id": "00006-caf99828-1f48-44af-92dc-0d08b4fdb2dc",
    "execution_millis": 1129,
    "execution_start": 1605009801896,
    "output_cleared": false,
    "source_hash": "51c65d4c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x114c9ffe0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the theta angle (main direction dZ\n",
    "nbs = 500\n",
    "x = np.rad2deg(np.arccos(a['PreDirectionLocal_Z']))\n",
    "fig3, ax3 = plt.subplots()\n",
    "n, bins, patches = ax3.hist(x, nbs, density=True, alpha=0.75, label='theta')\n",
    "ax3.set_xlim(160,180)\n",
    "ax3.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-01-23T19:55:19.844915Z",
     "start_time": "2024-01-23T19:55:19.555575Z"
    },
    "cell_id": "00007-9738eca9-ea76-4f04-9949-5ebdba81fec6",
    "execution_millis": 548,
    "execution_start": 1605009803028,
    "output_cleared": false,
    "source_hash": "f91cf92a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x111597fe0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the phi angle\n",
    "nbs = 200\n",
    "x = np.rad2deg(np.arctan2(a['PrePositionLocal_Y'], a['PrePositionLocal_X']))\n",
    "fig4, ax4 = plt.subplots()\n",
    "n, bins, patches = ax4.hist(x, nbs, density=True, alpha=0.75, label='phi')\n",
    "ax4.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "deepnote_execution_queue": [],
  "deepnote_notebook_id": "cffde93f-49bc-4a93-b8d3-146d7cad6d23",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
